Metal–organic frameworks (MOFs), tunable, nanoporous materials, are alluring recognition elements for gas sensing. Mimicking human olfaction, an array of cross-sensitive, MOF-based sensors could enable analyte detection in complex, variable gas mixtures containing confounding gas species. Herein, we address the question: given a set of MOF candidates and their adsorption properties, how do we select the optimal subset to compose a sensor array that accurately and robustly predicts the gas composition via monitoring the adsorbed mass in each MOF? We first mathematically formulate the MOF-based sensor array problem under dilute conditions. Instructively, the sensor array can be viewed as a linear map from gas composition space to sensor array response space defined by the matrix H of Henry coefficients of the gases in the MOFs. Characterizing this mapping, the singular value decomposition of H is a useful tool for evaluating MOF subsets for sensor arrays, as it determines the sensitivity of the predicted gas composition to measurement error, quantifies the magnitude of the response to changes in composition, and recovers which direction in gas composition space elicits the largest/smallest response. To illustrate, on the basis of experimental adsorption data, we curate MOFs for a sensor array with the objective of determining the concentration of CO2 and SO2 in the gas phase.
Robust, high-performance gas sensing technology has applications in industrial process monitoring and control, air quality monitoring, food quality assessment, medical diagnosis, and security threat detection.Nanoporous materials (NPMs) could be utilized as recognition elements in a gas sensor because they selectively adsorb gas. Imitating mammalian olfaction, sensor arrays of NPMs use measurements of the adsorbed mass of gas in a set of distinct NPMs to infer the gas composition. Modular and adjustable NPMs, such as metal-organic frameworks (MOFs), offer a vast materials space to sample for combinations to comprise a sensor array that produces a response pattern rich with information about the gas composition.Herein, we frame quantitative gas sensing, using arrays of NPMs, as an inverse problem, which equips us with a method to evaluate the fitness of a proposed combination of NPMs in a sensor array. While the (routine) forward problem is to use an adsorption model to predict the mass of gas adsorbed in the NPMs when immersed in a gas mixture of a given composition, the inverse problem is to predict the gas composition from the observed mass of adsorbed gas in each NPM. The fitness of a given combination of NPMs for gas sensing is then determined by the conditioning of its inverse problem: the prediction of the gas composition provided by a fit (unfit) combination of NPMs is insensitive (sensitive) to inevitable errors in the measurements of the mass of gas adsorbed in the NPMs. For illustration, we use experimentally measured adsorption data to analyze the conditioning of the inverse problem associated with a [IRMOF-1, HKUST-1] CH 4 /CO 2 sensor array. File list (2)download file view on ChemRxiv mof_sensing_inverse_problem_SI.pdf (2.78 MiB) download file view on ChemRxiv mof_sensing_inverse_problem.pdf (9.08 MiB)
Robust, high-performance gas sensing technology has applications in industrial process monitoring and control, air quality monitoring, food quality assessment, medical diagnosis, and security threat detection. Nanoporous materials (NPMs) could be utilized as recognition elements in a gas sensor because they selectively adsorb gas. Imitating mammalian olfaction, sensor arrays of NPMs use measurements of the adsorbed mass of gas in a set of distinct NPMs to infer the gas composition. Modular and adjustable NPMs, such as metal-organic frameworks (MOFs), offer a vast materials space to sample for combinations to comprise a sensor array that produces a response pattern rich with information about the gas composition.<br><br>Herein, we frame quantitative gas sensing, using arrays of NPMs, as an inverse problem, which equips us with a method to evaluate the fitness of a proposed combination of NPMs in a sensor array. While the (routine) forward problem is to use an adsorption model to predict the mass of gas adsorbed in the NPMs when immersed in a gas mixture of a given composition, the inverse problem is to predict the gas composition from the observed mass of adsorbed gas in each NPM. The fitness of a given combination of NPMs for gas sensing is then determined by the conditioning of its inverse problem: the prediction of the gas composition provided by a fit (unfit) combination of NPMs is insensitive (sensitive) to inevitable errors in the measurements of the mass of gas adsorbed in the NPMs. For illustration, we use experimentally measured adsorption data to analyze the conditioning of the inverse problem associated with a [IRMOF-1, HKUST-1] CH<sub>4</sub>/CO<sub>2</sub> sensor array.
Metal-organic frameworks (MOFs)-- tunable, nano-porous materials-- are alluring recognition elements for gas sensing. Mimicking human olfaction, an array of cross-sensitive, MOF-based sensors could enable analyte detection in complex, variable gas mixtures containing confounding gas species. Herein, we address the question: given a set of MOF candidates and their adsorption properties, how do we select the optimal subset to compose a sensor array that accurately and robustly predicts the gas composition via monitoring the adsorbed mass in each MOF? We first mathematically formulate the MOF-based sensor array problem under dilute conditions. Instructively, the sensor array can be viewed as a linear map from <i>gas composition space</i> to <i>sensor array response space</i> defined by the matrix <b>H</b> of Henry coefficients of the gases in the MOFs. Characterizing this mapping, the singular value decomposition of <b>H </b>is a useful tool for evaluating MOF subsets for sensor arrays, as it determines the sensitivity of the predicted gas composition to measurement error, quantifies the magnitude of the response to changes in composition, and recovers which direction in gas composition space elicits the largest/smallest response. To illustrate, on the basis of experimental adsorption data, we curate MOFs for a sensor array with the objective of determining the concentration of CO<sub>2</sub> and SO<sub>2</sub> in the gas phase.
Metal-organic frameworks (MOFs)-- tunable, nano-porous materials-- are alluring recognition elements for gas sensing. Mimicking human olfaction, an array of cross-sensitive, MOF-based sensors could enable analyte detection in complex, variable gas mixtures containing confounding gas species. Herein, we address the question: given a set of MOF candidates and their adsorption properties, how do we select the optimal subset to compose a sensor array that accurately and robustly predicts the gas composition via monitoring the adsorbed mass in each MOF? We first mathematically formulate the MOF-based sensor array problem under dilute conditions. Instructively, the sensor array can be viewed as a linear map from <i>gas composition space</i> to <i>sensor array response space</i> defined by the matrix <b>H</b> of Henry coefficients of the gases in the MOFs. Characterizing this mapping, the singular value decomposition of <b>H </b>is a useful tool for evaluating MOF subsets for sensor arrays, as it determines the sensitivity of the predicted gas composition to measurement error, quantifies the magnitude of the response to changes in composition, and recovers which direction in gas composition space elicits the largest/smallest response. To illustrate, on the basis of experimental adsorption data, we curate MOFs for a sensor array with the objective of determining the concentration of CO<sub>2</sub> and SO<sub>2</sub> in the gas phase.
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